Shapes: Their Clustering and Evolution

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Grouping similar objects into mutually exclusive groups is one of the most fundamental methods of knowledge discovery. Before the modern era the world was studied mostly qualitatively, and qualitative grouping was used to extract knowledge from the universe. For example, Aristotle divided living organisms into two groups, plants and animals, and divided animals into three groups according to how they moved: walking, flying, or swimming. Galileo used the similarity of movement of groups of stars and discovered that they are positioned in the same galaxy, which today is called the Milky Way. Mendeleev discovered the periodic table by grouping elements having similar chemical characteristics. Darwin studied the evolution of species by grouping biological bodies. Modern measurement systems allows collecting massive data. Cluster analysis or clustering refers to methods of grouping similar subjects while data are available. We aim to develop clustering methodologies useful for analysis of many data sets, but we specifically target 3D image data. Nowadays 3D measurement are feasible and widely applied in medicine, computer vision, cosmology, etc. We propose to develop quantitative tools for grouping 3D shapes and tracking their evolution through time. It is known that cancerous cells deform at the early stage of the cancer development. As the cell shape data are available nowadays, we aim to isolate such cells using this method. Predicting more complicated biological and physical objects such as body, face, and galaxy has immediate applications in biology, criminology, and cosmology.